Fast Alternating Direction Multipliers Method by Generalized Krylov Subspaces

The Alternating Direction Multipliers Method (ADMM) is a very popular and powerful algorithm for the solution of many optimization problems. In recent years it has been widely used ill-posed inverse However, one its drawback possibly high computational cost, since at each iteration, requires large-scale least squares problem. this work we propose computationally attractive implementation ADMM, with particular attention to We significantly decrease cost by projecting original large scale problem into low-dimensional subspace means Generalized Krylov Subspaces (GKS). dimension projection space not an additional parameter method as increases iterations. construction GKS allows fast computations, regardless increasing size Several computed examples show good performances proposed method.